Atomic clocks maintain a stable rate by locking the frequency of their local oscillator to the frequency of a selected atomic transition. Since the frequency of an atomic transition is stable, reproducible and universal, atomic clocks are used as standards for frequency and time.
For these atomic clocks to function properly, a magnetic field (the C-field) must be applied on the atoms. A problem with presently available atomic clocks is that the C-field can change with time, causing changes in the clock rate. The C-field can change for several different reasons including aging and hysteresis of the shield material, environmental temperature fluctuations, variations of the external magnetic field, magnetization of the shields, mechanical shocks, and ageing of the electronic circuits. Furthermore, another problem arises because the C-field is not perfectly spatially uniform, causing problems in evaluating the exact rate of the clock. Spatial non-uniformities of the C-field can be caused by non-uniformities of the shield material, necessary compromises in the design such as space restrictions and access holes, and the presence of other magnetic materials.
Because the frequency inaccuracy of the atomic clock is strongly dependent on the C-field, some methods have been proposed to reduce the magnetic field sensitivity. These methods can be classified by the type of mitigation used to reduce the magnetic field sensitivity. Four of these classes are listed here.
A) Use atomic transitions with a weak frequency dependence on the C-field:
The Zeeman effect is a change of the frequency of atomic transitions as a function of the magnetic field. In most atoms, the Zeeman effect is linear for all but a few transitions, for which it is quadratic. Below a certain value of the magnetic field (atom and transition dependent), the frequency dependence of the transitions obeying the quadratic Zeeman effect is much smaller than the linear frequency dependence. Such transitions are therefore selected to operate the atomic clock. (Examples of atomic transitions obeying the quadratic Zeeman effect, the so-called 0-0 transitions, are: In cesium: the |3, 0>−4, 0> transition; this is also used in the definition of the SI second; in rubidium, the |1, 0>−2, 0> transition; in hydrogen: the |0, 0>−1, 0> transition.) The reduced sensitivity of the transition frequency on the C-field improves the stability of the clock against variations and non-uniformity of the C-field (see FIG. 4, transition labeled 0-0). However in some state-of-the-art clocks, the sensitivity is still too large. Another possibility is to use a large C-field at a value for which the frequency dependence of the transitions becomes null (De Marchi 1993). The selected transition is between the states |3, −1> and |4, −1> (shown as “−1, −1” in FIG. 4). This method suffers from the need to produce an extremely uniform C-field, which has not been done successfully yet.
B) Build very stable electronic circuits, use permanent magnets and use shielding to produce a stable C-field:
The reduction of possible changes of the C-field has also been addressed by attempting to stabilize the C-field using passive stabilization or active feedback. For a C-field generated by a current, the current can be stabilized to a constant value. Magnetic shielding is also used to mitigate magnetic field variations, and permanent magnets can be used to generate the C-field. All these methods suffer from a large sensitivity on the temperature. Temperature variations produce changes in the circuit, shields or magnets which affect the C-field.
C) Compensate using feedback from a measured value of the C-field:
Several methods have been proposed to measure the C-field and correct its value to keep it constant. One example is the “ac C-field” method (Stern 1992), which uses the average clock frequency measured with alternating polarities of the current producing the C-field. Another similar but simpler method proposes to use a dual frequency synthesizer (Rubiola 1993) to run a clock at a high C-field while simultaneously measuring the C-field.
Other methods involving some kind of adjustment to the C-field have been attempted (Lepek 1990; Rabian 1990; Stern 2003). However, it is known in the art that such C-field adjustments are not reliable (Barnes 1988), because after a C-field adjustment, the frequency often relaxes back to almost where it started. Most of such stability problems have been traced to the magnetic shields and their hysteresis effects and experts generally discourage C-field adjustments to fine tune the clock. All methods of this class suffer from these common problems: Measuring the C-field interferes with the operation of the clock and requires a complex system. If the current generating the C-field is varied, hysteresis causes linearity problems, making the active feedback system less reliable. As a result the rate of the atomic clock changes, decreasing its stability and accuracy, and thus the performance of the clock.
Yet other methods (Braun 2010) employ the idea of using a clock running on the end-transitions. Since the end-transitions are linearly dependent on local magnetic fields, an approach is taken to actively lock the local field to a pre-determined value. This approach involves sensing, and with feedback electronics, maintaining the local bias field at a constant value. Therefore, these methods use a measurement of the Zeeman splitting to control the C-field with a feedback circuit where the rf magnetic field applied for the measurement is very weak for minimal disturbance of the clock. These methods also suffer from an increased complexity of the system, do not provide compensation for the non-uniformity of the C-field, and require unreliable C-field adjustments.
D) Compensate using feed-forward:
Another technique is to provide a feed-forward mechanism based on the value of the C-field. For example, U.S. Pat. No. 7,439,814 (Happer 2008) proposes the “Multi-Coherent method”, which uses a combination of many microwave frequencies, radio frequencies or optical pumping to achieve multiple measurements simultaneously. However, it only reduces the dependence of the frequency on the C-field by 33% (by using an average of all mF states) and is a complex method to implement. Another description related to using feed-forward is found in the Hewlett-Packard 5062C “Cesium Beam Frequency Reference Training Manual” (November 1974). The microwave field used by the clock can be modulated with an rf signal to fine-tune its frequency. However, no indication is made on how to use this to improve the frequency stability of the clock using that system. Also, these two methods above suffer from problems associated with an increased complexity of the microwave synthesizer which affect the long-term frequency stability of the clock.
There remains a need in the art for methods of stabilizing the frequency of atomic clocks against C-field variations which does not suffers from the problems encountered in one or more of the four classes above.